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So this lecture is going to answer the question, why do we care about shapes?

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Well, this is an important question because all of the libraries, we will use work under the assumption

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that your data has a specific shape.

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If you store your data in any way you want without conforming to the API of those libraries, well then

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they just won't work as expected.

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So getting your shapes right is a must.

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Furthermore, I find that understanding shapes helps you visualize the data.

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Time series are generally very easy to visualize.

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In fact, you are probably visualizing a time series right now, such as the power of words.

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However, this becomes a bit more difficult when the time series is multidimensional.

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So considering the shapes of things helps you think about the data in a more real and physical way.

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So the Simplest Time series is a one dimensional time series, for example, the daily temperature over

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time.

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In this case, your data would be a one dimensional array.

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So if you have a time series of length T, then you would have an array of size t.

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You can think of this as an array that goes from left to right or from top to bottom.

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However, this is actually an illusion because in one dimension there is no concept of left and right

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or top and bottom.

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This only happens because we're representing a one dimensional thing on a two dimensional screen.

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In Pandas, data frames are two dimensional, while series objects are one dimensional.

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In either of these can be used to store a one dimensional time series.

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If you use a series, then your series would be a series of length T, but if you use the data frame,

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then it would be a table with T rows and one column.

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In other words, T by one.

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Now, this is where things might get tricky because technically this isn't required.

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You might ask why not store it as a one by T instead of a T by one?

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The answer is because it's typically our convention and it works nicely with the libraries we will use.

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Now, of course, the data frame is capable of holding multiple columns.

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So now suppose that you have a multidimensional time series, for example, the daily temperature in

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multiple cities.

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And suppose that you have the temperature for cities over a period of t days.

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Then your data frame would have the shape T by d.

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So again, y, t by d and not d by t.

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And again, the answer is because this is what works nicely with the libraries we use.

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And note that this might actually go against your intuition because when we plot a time series, we

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typically think of it as going from left to right.

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But in this case, we store the Time series going from top to bottom.

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So just remember that T by D is the convention.

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Now things can become even more tricky.

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Suppose that we have multiple time series, each with multiple dimensions.

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For example, suppose we're reading accelerometer data from your smartphone.

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You'd like to use this data to predict whether the user is walking, sitting or lying down.

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In this case, you might record acceleration in the X, Y, and Z dimensions.

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So you have D equals three.

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And suppose that each recording you take lasts two seconds and you sample at 50Hz.

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So each recording has 100 samples in total, which means T equals 100.

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And of course, this is machine learning.

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So you're going to have multiple training samples.

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Suppose that you collect 1 million samples of users walking, sitting or lying down.

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In this case, we introduce a new letter N which by convention we will use for the number of samples

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in a dataset.

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So n equals 1 million.

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We have 1 million samples of users walking, sitting or lying down.

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In this case, our convention is to organize our data in an array of size.

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N by T by.

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So it's a number of samples by number of time, steps by number of dimensions.

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Now, again, you might be wondering why not a D, by T, by N or T, by n, by D.

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And again, the answer is because this is what our libraries expect in other libraries and other languages,

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things might work a different way.

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So it's always good to be cognizant of what convention is being used.

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And that's just part of your job as a data scientist.

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So when we say n by T by D recognize that this has three dimensions.

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In other words, you can think of it like a box in 3D space.

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I always try to encourage students to automatically think of a box whenever they hear n by ID.

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This is because just saying n by t by can be a bit abstract, but a box is clearly very physical and

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easy to visualize.

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So try to make this a reflex in your life will become much easier.

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So another reason this is useful is because your computer screen is only two dimensional.

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So suppose you had a three dimensional array in your computer and then you printed it out.

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Well, what would happen?

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The answer is that you would lose this 3D structure because your screen is only 2D.

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So you can see here that it just looks like nonsense.

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The printout doesn't give me any insight because it flattens a 3D object onto a 2D screen.

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This is unlike a 1D array and a 2D array where printing things out can be very useful.

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And I always have this motto that I tell students when in doubt, print it out.

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This usually always helps, but when you have a 3D array, not so much.

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But in any case, I hope you agree that thinking of shapes is very helpful both for intuition and also

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to prevent you from making errors when writing code.